Question

A ladder 10ft long rests against a vertical wall. If the bottom on the ladder slides away from the wall at 2 ft/s, how fast is the angle ladder makes with the ground changing when the bottom of the ladder is 5 ft from the wall.

Answer 1

Let the foot be x ft from the wall, let the angle formed by the ladder at the ground be Ø

given: dx/dt = 2 ft/s
find: dØ/dt when x = 5

x/10 = cosØ
x = 10cosØ
dx/dt = -10sinØ dØ/dt

when x=5,
height^2 + 5^2 = 10^2
height = √75

2 = -10(√75/10) dØ/dt
dØ/dt = - 2/√75 radians/second
= appr. - .23 rad/s

Answer 2

100mph